Area of Equilateral Triangle

In this page area of equilateral triangle we are going to see how to find the area of triangle. We have shown the formulas used to be find the area of the triangle, examples to understand this topic.

Formula:

     Area of Equilateral-triangle = (√3/4) a²

Here "a" represent the length of side of a triangle.

Example 1:

Find the area of the equilateral-triangle having the length of the side equals 10 cm

This problem can be done in two ways. We have shown those two methods one by one. In the first method we have used the above formula  to solve this problem. But in the second method we have used  the formula (1/2) x b x h to find the area.

Method 1:

Area of equilateral triangle = (√3/4) a²

Here a = 10 cm

                                    = (√3/4) (10)²

                                    = (√3/4) x (10) x (10)

                                     = (√3) x (5) x (5)

                                     =  25 √3 cm²

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Method 2:

Here the side length 10 cm refers the measurement of each side of a triangle. Let us consider the triangle ABC. In this triangle the length of each side that is AB,BC and CA are measuring 10 cm

In the above triangle the measurement of the side DC is 5 cm. In the triangle ADC , the side AC is called hypotenuse side whose length is 10 cm.

So we can say AC² = AD² + DC²

                     10² = AD² + 5²

                    100 = AD² + 25

                    100 - 25 = AD²

                        AD² = 75

                       AD = √75

                       AD = 5√3

Now we can apply the formula to find the area of the triangle that is (1/2) x base x height

Here base is 10 cm and height is 5√3 cm

Area of the given triangle = (1/2) x 10 x 5√3

                                   =  5 x 5√3

                                   = 25√3  cm²   

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Related Topics

• Perimeter of sector
  
• practice questions with solution
• Length of arc
• Practice questions on length of arc
  
• Perimeter of square 
• Perimeter of parallelogram
• Perimeter of rectangle
• Perimeter of triangle
• Area of a circle
• Area of Semicircle
• Area of Quadrant
  
• Area of sector
  
• Area of triangle
• Area of scalene triangle
  
• Area of square
  
• Area of rectangle
• Area of parallelogram
• Area of rhombus
• Area of trapezium
• Area of quadrilateral
  
• Area around circle
• Area of pathways
• Area of combined shapes
  

Area of Equilateral Triangle to Formulas for Shapes